Limit Theorems for Random Walks in the Hyperbolic Space

V. D. Konakov; S. Menozzi

doi:10.1134/S0001434625030083

Limit Theorems for Random Walks in the Hyperbolic Space

V. D. Konakov
, S. Menozzi

National Research University
Université d'Evry Val d'Essonne

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

1 Citation (Scopus)

Résumé

Abstract: A local limit theorem for random walks in the hyperbolic Poincaré space of dimension is proved. To this end, we use the model of a ball and describe the walk in it by means of the Möbius addition and multiplication. This also enables us to derive the corresponding law of large numbers.

langue originale	Anglais
Pages (de - à)	425-441
Nombre de pages	17
journal	Mathematical Notes
Volume	117
Numéro de publication	3
Les DOIs	https://doi.org/10.1134/S0001434625030083
état	Publié - 1 avr. 2025
Modification externe	Oui

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title = "Limit Theorems for Random Walks in the Hyperbolic Space",

abstract = "Abstract: A local limit theorem for random walks in the hyperbolic Poincar{\'e} space of dimension is proved. To this end, we use the model of a ball and describe the walk in it by means of the M{\"o}bius addition and multiplication. This also enables us to derive the corresponding law of large numbers.",

keywords = "hyperbolic space, local limit theorems, random walks and Brownian motion",

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AU - Konakov, V. D.

AU - Menozzi, S.

N1 - Publisher Copyright: © Pleiades Publishing, Ltd. 2025.

PY - 2025/4/1

Y1 - 2025/4/1

N2 - Abstract: A local limit theorem for random walks in the hyperbolic Poincaré space of dimension is proved. To this end, we use the model of a ball and describe the walk in it by means of the Möbius addition and multiplication. This also enables us to derive the corresponding law of large numbers.

AB - Abstract: A local limit theorem for random walks in the hyperbolic Poincaré space of dimension is proved. To this end, we use the model of a ball and describe the walk in it by means of the Möbius addition and multiplication. This also enables us to derive the corresponding law of large numbers.

KW - hyperbolic space

KW - local limit theorems

KW - random walks and Brownian motion

UR - https://www.scopus.com/pages/publications/105008237365

U2 - 10.1134/S0001434625030083

DO - 10.1134/S0001434625030083

M3 - Article

AN - SCOPUS:105008237365

SN - 0001-4346

VL - 117

SP - 425

EP - 441

JO - Mathematical Notes

JF - Mathematical Notes

IS - 3

ER -

Limit Theorems for Random Walks in the Hyperbolic Space

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